I believe that the stability of vector bundles or coherent sheaves (defined as the inequality of 'slopes' of its subsheaves) comes naturally from GIT. However, in any literature I can find, it is introduced in a way that consider the family of semi-stable bundles first and take the GIT quotient. I see this is technically necessary as we need some boundedness, but can we naturally deduce this definition from the GIT quotient (without any inequality on slopes given a priori)?
2026-03-25 15:59:04.1774454344
Stability of vector bundles as GIT quotient
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